Practical use of the first fundamental Gauss theorem results in the system of residual classes

Abstract

The method of determining the real remainder of a complex integer with respect to a complex modulus is considered in the paper. The method is based on the results of the first fundamental Gauss theorem. The examples of the definition of residues in a complex number domain are given. On the basis of the method, the algorithm for determining the real residue of an integer complex number by a complex module has been developed. Accordingly, the device for its technical implementation has been synthesized. The device has received a patent of Ukraine for an invention that confirms the novelty and practical value of the research results. The obtained results can be used for implementing tasks and algorithms in the residual class system (RCS) in the complex number area. The results can be used for the processing complex numbers in RCS as well. The method allows increasing the efficiency of practical use of RCS in the implementation of integer operations in the complex number area.